### Table of Contents

# ARCHIVE

# PH671: Solid State Physics - Electron Transport Module

# Archive from Fall 2011

PH671 is a two-credit graduate course taught by the Department of Physics at Oregon State University.

In 2011 the course is being taught Weeks 6 - 10 of Fall Quarter by Prof. Ethan Minot. The module is offered biyearly.

## Calendar

Day | Topic | Reading | Summary | Assignments | ||
---|---|---|---|---|---|---|

1 | M 10/31 | Sommerfield model | A&M Ch 2-3, Kittel Ch 6 | Gas of free electrons trapped in a 3d potential. Fermi Energy. Orders of magnitude. Introduce periodic potential. | HW #1 | |

2 | W 11/2 | Bloch Theorem & Semiclassical Dynamics | A&M Ch 8 & Ch 12 | Bloch wave states. Occupation function. Semiclassical equations for velocity and dk/dt. Resistivity of a metal. Resistivity of a semiconductor. Relaxation time. Mobility. | - | |

3 | F 11/4 | Boltzmann Transport Eqn | A&M Ch 13 | Phonon review (ph575 notes24). Fermi Golden Rule review. Transition matrix element for electron-phonon interaction. Conservation of momentum/energy. Scattering probability. Example of temperature dependent resistivity in metals. | hw1soln.pdf | |

Day | Topic | Reading | Summary | Assignments | ||

4 | M 11/7 | Ballistic conduction | Kittel Ch18 | day4.pdf:Quantum coherence destroyed by inelastic scattering. Current through a 1d wire. Quantum of conductance. One elastic scattering site in a 1d wire. Alternative reading Chpt 4 of Harmans | HW #2 | |

5 | W 11/9 | Localization | Kittel Ch18 | day5.pdf: Transmission probability for a pair of elastic scattering centers in a 1d wire. Localization caused by random distribution of elastic scattering sites. Alternative reading Chpt 4 of Harmans | - | |

6 | F 11/11 | Crossover to diffusive transport | Kittel Ch18 | day6.pdf: Transmission probability for pair of inelastic scattering sites. Resistance of many inelastic scattering sites is series (diffusive transport). Research example: Transition between localization and diffusive transport in CNTs. Alternative reading Chpt 4 of Harmans | hw2soln.pdf | |

Day | Topic | Reading | Summary | Assignments | ||

7 | M 11/14 | Other conduction/ insulation mechanims | Variable range hopping, Mott insulators (review metal with half filled band, ph575 notes5,ph575 notes6) | HW #3 | ||

8 | W 11/16 | Mott Transition | Kittel or A&M | Thomas-Fermi screening for metals with small lattice constants. Polarizabiliy of Mott insulators with large lattice constants. Critical lattice constant for Mott transition. Intro to topological phenomena in solid state. Review of classical Hall Effect. | - | |

9 | F 11/18 | AB Effect, QHE | Feynman Lecture 15-9 | Magnetic vector potential cause phase shift in wavefunction (review of fundamental QM). Analyze the AB experiment for electrons in vacuum. Define the flux quanta. Examine the IBM experiment showing AB Effect in a normal metal ring. Energy spectra of Landau levels in a 2DEG. Evolution of density of states as B field is increased. | hw3soln.pdf | |

Day | Topic | Reading | Summary | Assignments | ||

10 | M 11/21 | QHE | Course notes | Experimental geometry. Scattering suppressed when D(E_F) = 0. Drift in crossed E and B fields. Ratio of current to Hall voltage. Discussion of topological interpretation. | HW #4 | |

11 | W 11/23 | Tunneling | Kittel Ch 18 | Scanning tunneling microscope (STM). Metal work functions. Application of WKB to STM. dI/dV_tip proportional to density of states. Research example, gapmap.pdf. Tunnel Magnetoresistance. Calculating ΔR/R_0. handout11.pdf | - | |

12 | F 11/25 | THANKSGIVING HOLIDAY | hw4soln.pdf | |||

Day | Topic | Reading | Summary | Assignments | ||

13 | *M 11/28 | *Superconductivity | Ch 10 Ibach & Luth pdf | Experimental observations. Cooper pair wavefunction (equal & opposite k). *Ethan traveling to PSU to present colloquium | HW #5 | |

14 | W 11/30 | Superconductivity | Ch 10 Ibach & Luth | Number of Cooper Pairs in system. Temperature dependent strength of Cooper Pair binding. Relationship between T_c and atomic mass. Macroscopic wavestate. London equation. Calculate critical B-field. | - | |

15 | F 12/2 | Superconductivity | Ch 10 Ibach & Luth | Comparison between Type I and Type II superconductors. Intro to Ginzburg-Landau Theory. Images of vortex lattices. Note: Kittel Ch 10 is also a good reference. Overview of superconducting devices. Analysis of a Josephson Junction and the precision frequency to voltage converter. | hw5soln.pdf |

Readings not used this quarter:

## Syllabus

Fundamentals of bandstructure

- Bloch theorem
- Semiclassical dynamics

Boltzman transport equation

- motion in constant E field → Drude result
- diffusion
- phonon scattering mechanism

Quantum transport

- elastic vs inelastic scattering
- 1d wire no scattering (nano module?)
- Landauer formalism

Quantum to classical crossover

- Transmission probabilities
- Resonant tunneling
- Incoherent scattering

Transport in magnetic field

- Vector potential and electron phase
- Example: AB effect

Localization

- Feynman path integrals in solid state
- Anderson localization in different dimensions
- Testing with B-field

Metal-Insulator transition

- Difference between Mott insulator and Anderson localization (not covered in 2009)
- Thomas-Fermi screening
- Bohr radius overlap

Tunneling

- WKB approx
- STM (nano module?)
- Fermi golden rule
- Coulomb blockade (nano module?)

Superconductivity

- curl A = 0 inside superconductor
- consequences

### Archive

Webpages from previous years